| Full text | |
| Author(s): |
Aragao-Costa, E. R.
Total Authors: 1
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| Document type: | Journal article |
| Source: | ANNALS OF FUNCTIONAL ANALYSIS; v. 10, n. 2, p. 262-276, MAY 2019. |
| Web of Science Citations: | 0 |
| Abstract | |
In this article we give sufficient conditions for the hypoellipticity in the first level of the abstract complex generated by the differential operators L-j = partial derivative/partial derivative t(j) + partial derivative phi/partial derivative t(j) (t, A)A, j = 1, 2, ..., n, where A : D(A) subset of X -> X is a sectorial at operator in a Banach space X, with R sigma(A) > 0, and phi = phi(t, A) is a series of nonnegative powers of A(-1) with coefficients in C-infinity(Omega), Omega being an open set of R-n with n is an element of N arbitrary. Analogous complexes have been studied by several authors in this field, but only in the case n = 1 and with X a Hilbert space. Therefore, in this article, we provide an improvement of these results by treating the question in a more general setup. First, we provide sufficient conditions to get the partial hypoellipticity for that complex in the elliptic region. Second, we study the particular operator A = 1 - Delta : W-2,W-p(R-N) subset of L-P(R-N) -> L-p(R-N), for 1 <= p <= 2, which will allow us to solve the problem of points which do not belong to the elliptic region. (AU) | |
| FAPESP's process: | 14/02899-3 - Global solvability for differential complexes and converse to the theorem of the existence of Lyapunov function to gradient-like evolution process |
| Grantee: | Éder Ritis Aragão Costa |
| Support Opportunities: | Regular Research Grants |